Step by step
The question
Question: find x.
The two lines are parallel.
The alternate angles are 3x + 10 and 70°.
1 Use the angle fact
The arrows show the two lines are parallel.
Parallel lines go the same way.
They never meet.
A third line crosses both of them.
It is called a transversal.
Our two angles are between the parallel lines, on opposite sides of the transversal.
They are called alternate angles.
Together they make a Z shape.
Alternate angles are equal.
Why?
Look at this angle at the top.
It is in the same place as the bottom angle, so they are equal.
It is also opposite our top angle, so they are equal too.
So the two angles are equal: 3x + 10 = 70.
We want x by itself.
Two things are stuck to x: times 3 and + 10.
The + 10 is on the outside, so it comes off first.
Then the times 3.
2 Remove the + 10
To remove + 10, we take away 10.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
+ 10 and − 10 make zero.
Cross them out.
70 − 10 = 60.
Now we have 3x = 60.
3 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
60 divided by 3 is 20.
So x = 20!
4 Check
Let's check: put x = 20 in each angle.
We get 70°, the same as the other angle.
So x = 20 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 10.
Then: remove the 3.
Last: check.